The mirror person is the self that Deren wants to destroy-because it is completely mirror, and its connotation is that this self is shaped by others (husband), lacks independence, and is one of Deren's self-system Alien, she (or rather, they, Deren's other selves) wants to destroy it. This is implied by the appearance of the husband's face in the mirror at the end of the film—this self emerges according to the husband's desires.
Flowers represent marriage, or relationships. Her husband would send her flowers and put them in front of her bed, but this romantic act was the beginning of Deren's nightmare, and it was a beautiful imprisonment for her.
The key represents reconciliation with the "self". The repetitions in the dream are Deren's constant attempts to reconcile with herself. However the attempt failed. She holds the key to open the door, but is unable to reach reconciliation with "It" (the Mirror Man). So on the next cycle, the key becomes the knife, and she becomes "them"—they join forces to strangle the it.
This movie reminds me of Charlotte Perkins Gilman's the yellow wallpaper. In a male-dominated relationship, women are ultimately unable to accept the intrusion of an objectified self, unable to reconcile with the constituted self, and eventually go crazy or even perish.
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